In the method of wire-cutting a workpiece by electroeroerosion, a continuous wire electrode is axially transported from a supply means to a collection means. In the path of wire travel, a pair of machining guide members are commonly disposed at opposite sides respectively of the workpiece to stretch the traveling wire electrode linearly thereacross, thus traversing the workpiece and, positioning the traveling wire electrode in a machining relationship with the workpiece. The apparatus includes a power supply for passing an electrical machining current, typically in the form of a succession of pulses, between the wire electrode and the workpiece across a machining gap flooded with a machining liquid, e.g. water, to electoerosively remove material from the workpiece. As the material removal proceeds, the workpiece is displaced transversely relative to the axis of the wire electrode along a prescribed feed path so that a desired cut is formed in the workpiece. The operation commonly requires, in advance, threading or passing the continuous wire electrode through the unmachined workpiece.